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Zapiski Nauchnykh Seminarov POMI, 2017, Volume 461, Pages 107–123 (Mi znsl6483)  
This article is cited in 4 scientific papers (total in 4 papers)

Justification of the wavelet-based integral representation of a solution of the wave equation

E. A. Gorodnitskiy, M. V. Perel

St. Petersburg State University, St. Petersburg, Russia
Full-text PDF (238 kB) Citations (4)
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Abstract: We study the previously obtained integral representation of a solution of the wave equation. The integrand contains the weighted localized solutions of the wave equation, which depend on integration variables. We construct the parameterized family of the localized solutions from the chosen one by employing the transformations of shift, dilation and the Lorentz transform. We give the sufficient conditions of the pointwise convergence for the obtained improper integral. The convergence in the $\mathcal L_2$ sense is proven too.
Key words and phrases: wave equation, integral representations, wavelet analysis, the affine Poincaré group.
Funding agency Grant number
Saint Petersburg State University 11.42.1073.2016
Received: 01.11.2017
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 238, Issue 5, Pages 630–640
DOI: https://doi.org/10.1007/s10958-019-04262-5
Document Type: Article
UDC: 517.958+517.444+512.815.8+517.986.6
Language: Russian
Citation: E. A. Gorodnitskiy, M. V. Perel, “Justification of the wavelet-based integral representation of a solution of the wave equation”, Mathematical problems in the theory of wave propagation. Part 47, Zap. Nauchn. Sem. POMI, 461, POMI, St. Petersburg, 2017, 107–123; J. Math. Sci. (N. Y.), 238:5 (2019), 630–640
Citation in format AMSBIB
\Bibitem{GorPer17}
\by E.~A.~Gorodnitskiy, M.~V.~Perel
\paper Justification of the wavelet-based integral representation of a~solution of the wave equation
\inbook Mathematical problems in the theory of wave propagation. Part~47
\serial Zap. Nauchn. Sem. POMI
\yr 2017
\vol 461
\pages 107--123
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6483}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 238
\issue 5
\pages 630--640
\crossref{https://doi.org/10.1007/s10958-019-04262-5}
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  • https://www.mathnet.ru/eng/znsl/v461/p107
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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